Can the web client run on https?

I am attempting to embed my live map/law page into a website. however, the website requires all embedded sites to be in https. Is there a way that I can make our law page hosted in HTTPS instead of http?

The best way to do this would be to let the server only listen on loopback and use a reverse proxy such as Nginx to do the encryption. This is a generally safer approach when exposing custom web applications to the public internet, anyway, as you can more easily control what kind of requests are allowed.